# Lesson 18

Expressions with Rational Numbers

Let’s develop our signed number sense.

### Problem 1

The value of \(x\) is \(\frac {\text{-}1}{4}\). Order these expressions from least to greatest:

\(x\)

\(1-x\)

\(x-1\)

\(\text-1\div x\)

### Problem 2

Here are four expressions that have the value \(\frac {\text{-}1}{2}\):

\(\frac {\text{-}1}{4} + \left(\frac {\text{-}1}{4}\right)\)

\(\frac12 - 1\)

\(\text-2 \boldcdot \frac14\)

\(\text-1 \div 2\)

Write five expressions: a sum, a difference, a product, a quotient, and one that involves at least two operations that have the value \(\frac {\text{-}3}{4}\).

### Problem 3

Find the value of each expression.

- \(\text-22 + 5\)
- \(\text-22 -(\text-5)\)
- \((\text-22) (\text-5)\)
- \(\text-22 \div 5\)

### Problem 4

The price of an ice cream cone is $3.25, but it costs $3.51 with tax. What is the sales tax rate?

### Problem 5

Here are 4 points on a coordinate plane.

- Label each point with its coordinates.
- Plot a point that is 3 units from point \(K\). Label it \(P\).
- Plot a point that is 2 units from point \(M\). Label it \(W\).

### Problem 6

A furniture store pays a wholesale price for a mattress. Then, the store marks up the retail price to 150% of the wholesale price. Later, they put the mattress on sale for 50% off of the retail price. A customer just bought the mattress on sale and paid $1,200.

- What was the retail price of the mattress, before the discount?
- What was the wholesale price, before the markup?